Lecture 10General ConceptSlide 3A More Realistic ScenarioSmall DisplacementSlide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Large DisplacementSlide 17Slide 18Slide 19Slide 20Slide 21Idea of Previous SlidesAtmospheric StabilitySlide 24Slide 25Two CasesLapse RatesStabilityGraphical DepictionSaturated AirGeneral ResultContinuedSlide 33ApplicationExample: Mid-Level CloudsAltocumulusAltostratusDeep ConvectionPhysics Review: EnergySlide 40Slide 41It Can Be Shown …Available Potential EnergySlide 44Energy BarriersSlide 46Slide 47CAPE, CINSlide 49Slide 50Isolated Severe ThunderstormsSudden Outbreaks of Severe WeatherSlide 53Slide 54Level of Free Convection (LFC)Equilibrium Level (EL)Convective Inhibition (CIN)Slide 58CAPESlide 60Lecture 10Lecture 10Static StabilityStatic StabilityGeneral ConceptGeneral ConceptAn equilibrium state can be stable or An equilibrium state can be stable or unstableunstableStable equilibrium: A displacement induces a Stable equilibrium: A displacement induces a restoring force restoring force i.e., system tends to move back to its original i.e., system tends to move back to its original statestateUnstable equilibrium: A displacement Unstable equilibrium: A displacement induces a force that tends to drive the induces a force that tends to drive the system even further away from its original system even further away from its original statestateA More Realistic ScenarioA More Realistic ScenarioEquilibriumSmall DisplacementSmall DisplacementSmall DisplacementSmall DisplacementSmall DisplacementSmall DisplacementSmall DisplacementSmall DisplacementSmall DisplacementSmall DisplacementSmall DisplacementSmall DisplacementSmall DisplacementSmall DisplacementSmall DisplacementSmall DisplacementSmall DisplacementSmall DisplacementSmall DisplacementSmall DisplacementSmall DisplacementSmall DisplacementStable.Large DisplacementLarge DisplacementLarge DisplacementLarge DisplacementLarge DisplacementLarge DisplacementLarge DisplacementLarge DisplacementLarge DisplacementLarge DisplacementLarge DisplacementLarge DisplacementUnstable.Idea of Previous SlidesIdea of Previous SlidesThere may be a critical displacement There may be a critical displacement magnitudemagnitudedisplacement < critical displacement < critical  stable stabledisplacement > critical displacement > critical unstableunstable(More about this shortly)(More about this shortly)Atmospheric StabilityAtmospheric StabilityUnsaturated AirUnsaturated AirConsider a vertical parcel displacement, Consider a vertical parcel displacement, zzAssume displacement is (dry) adiabaticAssume displacement is (dry) adiabaticChange in parcel temperature = -Change in parcel temperature = -d d zzDenote lapse rate of environment by Denote lapse rate of environment by zParcelT = T0T=T0 - dzEnvironmentT = T0T = T0 - zTemp of displaced parcel  temp of environmentTwo CasesTwo CasesParcel temp. > environment temp. Parcel temp. > environment temp.  parcel less dense than environmentparcel less dense than environment  parcel is buoyantparcel is buoyantParcel temp. < environment temp.Parcel temp. < environment temp.  parcel denser than environment parcel denser than environment  parcel is negatively buoyantparcel is negatively buoyantLapse RatesLapse RatesTTparcelparcel = T = T00 - - ddzzTTenvenv = T = T00 - - zzTTparcelparcel > T > Tenvenv if T if T00 - - ddz > Tz > T00 - - zz   > > ddTTparcelparcel < T < Tenvenv if T if T00 - - ddz < Tz < T00 - - zz   < < ddStabilityStability > > d d  resultant force is positive resultant force is positive parcel acceleration is upward (away from parcel acceleration is upward (away from original position)original position) equilibrium is unstableequilibrium is unstable < < d d  resultant force is negative resultant force is negative parcel acceleration is downward (toward parcel acceleration is downward (toward original position)original position) equilibrium is stableequilibrium is stableGraphical DepictionGraphical DepictionTemperaturezTemp of rising parcelStable lapse rateUnstable lapse rateSaturated AirSaturated AirRecall: Vertically displaced parcel Recall: Vertically displaced parcel cools/warms at smaller ratecools/warms at smaller rateCall this the moist-adiabatic rate, Call this the moist-adiabatic rate, mmPrevious analysis same with Previous analysis same with dd replaced replaced by by mmEquilibrium stable if Equilibrium stable if  < < mmEquilibrium unstable if Equilibrium unstable if  > > mmGeneral ResultGeneral ResultSuppose we don’t know whether a layer of Suppose we don’t know whether a layer of the atmosphere is saturated or notthe atmosphere is saturated or not > > dd   > > mm  equilibrium is unstable, equilibrium is unstable, regardlessregardlessEquilibrium is Equilibrium is absolutely unstableabsolutely unstable < < mm   < < dd  equilibrium is stable, equilibrium is stable, regardlessregardlessEquilibriumEquilibrium is is absolutely stableabsolutely stableContinuedContinuedSuppose Suppose mm < <  < < ddLayer is stable if unsaturated, but unstable Layer is stable if unsaturated, but unstable if saturatedif saturatedEquilibrium is Equilibrium is conditionallyconditionally unstableunstablemdAbsolutely unstableAbsolutely stableConditionally unstableApplicationApplicationIf a layer is unstable and clouds form, they If a layer is unstable and clouds form, they will likely be cumuliformwill likely be cumuliformIf a layer is stable and clouds form, they If a layer is stable and clouds form, they will likely be stratiformwill likely be stratiformExample: Mid-Level CloudsExample: Mid-Level CloudsSuppose that clouds form in the middle Suppose that clouds form in the middle tropospheretroposphereUnstable Unstable  altocumulus altocumulusStable Stable  altostratus altostratusAltocumulusAltocumulusAltostratusAltostratusDeep ConvectionDeep ConvectionPrevious discussion not sufficient to Previous discussion not sufficient to explain thunderstorm